On a Micromechanical Basis of Stochastic Constitutive Laws

Abstract: A procedure for derivation of stochastic constitutive laws is outlined on the basis of graph-representable linear elastic microstructures. Central to the procedure is the concept of a scale dependent representative volume element, which leads to two response tensors convergent from above and below to the effective moduli of an infinite microstructure. In a given boundary value problem these response tensors are to be used to bound the effective solution at a given scale of resolution.